Modeling the Finite Deformation Anisotropic Viscoelastic Behavior of the Cornea

This paper presents the development of a finite element model for the cornea as a first step towards a physiologically based model to study the role of cornea and sclera biomechanics in glaucoma. We developed a finite-deformation anisotropic constitutive model of the cornea that considers the effects of the fibrilar microstructure on the viscoelastic stress response. The model was base on the hypothesis that the dominant mechanism for the tensile viscoelastic behavior of the cornea is the viscoelastic stretching of the collagen lamellae. This approach yielded two main results. First, the viscoelastic properties of the cornea are derivable directly from the viscoelastic properties of the collagen fibrils and proteoglycan matrix. Second, the anisotropy in the stress response and creep response are determined solely by the arrangement collagen lamellae, which depends on orientation and material position. This allows the model parameters that determines anisotropy to be obtained from microstructural characterizations, such as the X-ray diffraction experiments of Meek and coworkers [1], while the model parameters that determines viscoelasticity to be determined from mechanical experiments. For this initial work, the viscoelastic parameters were fitted to the uniaxial tensile strip tests [2] and inflation tests with digital image correlation (DIC) [3] of bovine cornea performed by our group. Since microstructural characterizations are not available for bovine cornea, we used the data of Aghamohammadzadeh et. al. [1] for the human cornea.